Victor Moses scored the winner at Turf Moor to pull Chelsea within five points of fourth-place Tottenham.
Chelsea emerged 2-1 winners over Burnley at Turf Moor on Thursday night, keeping their quest for a top-four finish alive.
The Clarets began their season by beating the Blues at Stamford Bridge on the opening day, and came into this one as the top flight's most in-form sides - off the back of a five-game winning streak - knowing that completing the double against the evening's opposition would all but solidify their place in a European spot, as well as take them above Arsenal into sixth place.
Antonio Conte, quite desperate to build on Saturday's win against Southampton, started both Alvaro Morata and Olivier Giroud up front and kept Eden Hazard on the bench. The Italian, though, was unable to field Marcos Alonso due to the Spaniard picking up a three-match ban for his challenge on Shane Long during the Saints victory.
Alonso's absence saw Emerson Palmieri make his first Premier League start for the Londoners since his January switch from AS Roma.
The Blues started rather brightly. Giroud looked a threat quite early on and linked up quite well with his strike partner Morata, who forced a save from Nick Pope from a tight ankle around 10 minutes in.
Their efforts would pay off during minute 19, when Victor Moses forced an own goal from defender Kevin Long with a cross from the right side. The Nigerian's attempt to find Giroud was thwarted by Pope, but it was hit straight into Long, who couldn't avoid knocking the ball into the back of his own net.
Morata nearly doubled the lead moments later after receiving a neatly-threaded through ball from Giroud, but Pope stepped up to get a touch on his attempted dink to put the ball out for a corner.
Conte's men went into halftime quite comfortably, but with the most marginal of leads. And coming on in the second half, they were just as dominant in the early going.
The Clarets were let off big time 10 minutes into the second period after N'Golo Kante released Morata with a neat pass from the Chelsea half that ultimately set him one-on-one with Pope. The Spaniard somehow missed the target, despite having enough time and space to pick his spot.
Replays later showed that Pope may have gotten the slightest of touches on the striker's shot.
The home side made the visitors pay for their wastefulness in the 64th minute, but it was as fortuitous as the own goal was for Chelsea, with Ashley Barnes deflecting a wayward shot from Johann Berg Gudmundsson off his heel and into the back of the Blues' net.
The Londoners were back in front just four minutes later, however, reclaiming their lead through a strike from Moses, following a whipped cross from Palmieri from the left flank.
Hazard came on for the last 20 minutes as an angry Morata made way, and the Belgian made a menace of himself in the attacking half.
The Blues were able to retain their lead past the 90 and after four minutes of stoppage time, bringing an end to Burnley's winning streak and keeping their 35-year unbeaten run at Turf Moor alive.
The victory brings them to within five points of fourth-placed Spurs, also keeping their Champions League hopes afloat.